Problem

Source: China Additional TST for IMO 2020, P4

Tags: number theory, Diophantine equation



Show that the following equation has finitely many solutions $(t,A,x,y,z)$ in positive integers $$\sqrt{t(1-A^{-2})(1-x^{-2})(1-y^{-2})(1-z^{-2})}=(1+x^{-1})(1+y^{-1})(1+z^{-1})$$